I think that you have not received an answer to this query because it doesn't have a simple answer. The parameters that you need to examine depend on the signaling protocol and your design requirements. Some SerDes protocols specify the relevant connector parameters for you. In general, you should look at signal referencing through the connector. Some connectors that are designed specifically for signal integrity performance have designated pins for return paths. The vendor will usually specify the effective signal path impedance in these cases. With this parameter, you can compare to your PCB trace target impedance for matching.
Connectors that are designed for multi-gigabit transmission will probably also include insertion loss (IL) specifications. If the IL is greater than -1dB at 1/2 your data rate, that is a good start. You might also want to look at the transmission between different pins, which is an indication of potential crosstalk. Before final selection, I would get a good simulation model from the connector vendor and simulate the nets of interest.
I would also recommend that you get some consulting help. There are various SI experts that you can contact. Also, the high-end connector vendors probably have some SI expertise to help you understand the advantages of their different connectors.